D-dependence of the gap between the critical temperatures in the one-dimensional gauge theories

Abstract

We investigate the dimensional dependence (D-dependence) of the difference (gap) between the critical temperatures associated with the uniform/non-uniform and non-uniform/gapped transitions in the large-N bosonic gauge theories with D matrix scalar fields on a S 1 -circled space. We use the equations describing these critical temperatures given in the 1/D expansion [1]. These transitions are related with Gregory-Laflamme instabilities in the gravities and Rayleigh-Plateau instabilities in the fluid dynamics, and qualitative similarities between these are expected. We find that the tendency in the D-dependence of the gap is opposite from those in the gravity and fluid side. This is interesting as a counterexample to the gauge/gravity and gauge/fluid correspondences. * shingo.portable(at)gmail.com 1). in [1], the second-order transition occurs first, then the third-order transition occurs next as of D = 9, 2). in [17], the third-order transition occurs first, then the second-order transition occurs next, at D = 9,3). in [49], only the first-order transition occurs until D = 20, then the transition switches to the situation in [1] at some large D.One thing we can say is that the conclusion in [17] is wrong. At present we cannot conclude whether [1] or [49] is right. For this purpose, we need to confirm the existence † The study to have formulated the 1/D expansion first is [48] in the IIB matrix model [18], and we can regard the work of [1] as its extension to a S 1 -circled space.

The nonperturbative phase diagram of the bosonic BMN matrix model

“…Our results are in a broad agreement with 1/D studies [17,25] but does not match it exactly as the authors observe two closely separated phase transitions. As a recent numerical study of the BFSS model [18] also reports a single phase transition, we believe that by including higher terms in the 1/D expansion, the two phase transitions would merge into a single one in this approximation as well.…”

The confining transition in the bosonic BMN matrix model

“…For the case with µ = 0, known as the bosonic BFSS model, there are already several studies in the literature. These include a perturbative expansion in 1/D [14,16,30], where D is the number of matrices (D = 9 in our case), and numerical studies [13][14][15]17]. Both the 1/D expansion [16] and earlier studies [13] reported two closely separated critical tem-JHEP06(2020)174…”

The Confining Transition in the Bosonic BMN Matrix Model

“…A straightforward calculation [6,7,28] shows that, in the large-N limit, there is a single phase transition with critical temperature T c = For the case with µ = 0, known as the bosonic BFSS model, there are already several studies in the literature. These include a perturbative expansion in 1/D [14,16,29], where D is the number of matrices (D = 9 in our case), and numerical studies [13,14,17]. Both the 1/D expansion [16] and earlier studies [13] reported two closely separated critical temperatures.…”